Electrostatics with Conductors
Introduced| English | Meaning |
|---|---|
| electrostatic equilibrium/ɪˌlektrəʊˈstætɪk ˌiːkwɪˈlɪbrɪəm/ | A condition in which charges have no net motion; in a conductor, its interior electric field is zero and it is at one potential. |
| Faraday cage/ˈfærədeɪ keɪdʒ/ | A conducting enclosure that shields its interior from external electric fields, particularly under electrostatic conditions. |
Why is a metal car one of the safest places in a lightning storm?
- Lightning hits the car, yet the people inside are unharmed.
- A conductor wraps its passengers in a charge-free, field-free space.
- The metal's free electrons rearrange in an instant to cancel the field inside.
- This lesson is about how conductors behave once the charges stop moving.
No field inside, in equilibrium
- Once charges settle (electrostatic equilibrium 静电平衡), the field inside a conductor is zero.
- If it weren't, the free charges would feel a force and keep moving — not settled.
- So $E = 0$ everywhere inside the metal.
- Any cavity inside is shielded too — that is a Faraday cage 法拉第笼.
Inside a conductor in electrostatic equilibrium, the electric field is:
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If it were not zero, free charges would move — so at equilibrium $E = 0$ inside.
A hollow conductor shields its inside from external fields (a Faraday cage).
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The conductor cancels the field inside the cavity — a Faraday cage.
All charge lives on the surface
- Because the inside field is zero, no net charge can sit inside.
- Every bit of excess charge is pushed to the surface.
- Gauss's law confirms it: any interior Gaussian surface encloses zero charge.
- The charge spreads to make the whole conductor one potential.
Excess charge on a solid conductor sits:
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With zero interior field, all excess charge must lie on the surface.
The field just outside
- Just outside the surface, the field is perpendicular to it.
- A parallel field would push surface charges sideways — but they've stopped.
- Its size is $E = \dfrac{\sigma}{\varepsilon_0}$, set by the local surface charge density $\sigma$.
- Flat inside, purely perpendicular outside.
A charged conductor at equilibrium
Sort each statement about a conductor in electrostatic equilibrium.
Just outside a conductor's surface, the field is ____ to the surface.
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A parallel component would move surface charges, so $E$ is perpendicular.
Select all true statements about a conductor in equilibrium.
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Zero interior field, surface charge, single potential. Charge never fills the volume.
Charge crowds at sharp points
- On a lumpy conductor, charge piles up where the surface curves sharply.
- Sharp points have the highest $\sigma$ and the strongest field.
- That is why lightning rods are pointed — the field there ionises the air first.
- Smooth, round shapes spread charge more evenly.
On a conductor, charge and field are strongest at:
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Charge crowds at sharp points, giving the highest $\sigma$ and field.
You sit inside a metal cage as a charged rod touches the outside.
- The charge spreads over the cage's outer surface.
- Inside, $E = 0$, so you feel nothing — the cage shields you.
"$E = 0$ inside" holds only in electrostatic equilibrium — after the charges have settled. During the split-second of rearranging, fields inside are not zero. And it applies to the conductor's material, not to a charge you place in a hollow cavity.
In electrostatic equilibrium a conductor has $E = 0$ inside, so all excess charge sits on the surface and the whole conductor is one potential. Just outside, $E = \sigma/\varepsilon_0$ and is perpendicular to the surface; charge crowds at sharp points.
Write from 12 microcoulomb on the surface
- A conductor in equilibrium carries 12 microcoulomb of excess charge.
- Say where that charge sits and what the field is inside the metal.
A conductor in electrostatic equilibrium has 12 microcoulomb of excess charge. Where is that charge, and what is the field inside the conducting material?
In equilibrium, excess charge moves until the field in the conductor is 0. That leaves the excess on the surface.
Where is the excess charge?
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Equilibrium forces the excess charge to the surface and makes the interior field 0.